关键词: Riesz 基;Euler-Bernoulli 梁, 边界控制, 稳定性

Abstract:

An Euler-Bernoulli beam equation subject to a special boundary feedback problem is considered. This problem is in sharp contrast to the general principle in engineering practice that the conjugate variables cannot be assigned simultaneously at the same boundary. The Riesz basis approach is adopted in investigation. It is shown that the closed-loop system is well-posed in the usual energy state space and the trajectory approaches to the zero eigenspace of the system as time goes to infinity. Therelease of the engineering restriction gives more freedom in the design of boundary controls for thesuppression of vibration of flexible structures.

Key words: Riesz basis, Euler-Bernoulli beam, boundary control, stability